Biomedical Engineering Reference
In-Depth Information
Coding of binary features
Let us describe the binary feature as any feature that could be present or absent in an
object but for which it is not possible to indicate its numerical value. For example,
for the binary feature “This word starts with the letter 'B',” the word “Blue” will
equal 1 and the word “Green” will equal 0. Let a certain class of objects be
described by the set of binary features
U
=(
u
1
,
,
u
k
), and let each object from
this class be represented in the form of the binary vector in which the component
i
equals 1 if the corresponding feature is present in the object.
Let the neural network utilized for recognition have
n
neurons. The presence of
the feature
i
is coded by the excitation of
m
neurons. For each feature, the neurons
that are excited upon the appearance of this feature are selected with the aid of a
random procedure. We introduce a binary vector that contains “1” corresponding to
the excited neurons and “0” corresponding to the non-excited neurons. Let us term
this binary vector the mask of the corresponding feature and denote the mask of
feature
i
with
M
i
. If the object contains several features
i
,
j
,
k
, then the mask of
Z
is
defined as a bitwise logical “OR” of the corresponding masks:
...
Z
¼
M
i
U
M
j
U
M
k
:
(6.11)
Coding the feature position on the image
Let us examine the handwritten symbol located on the image in the window having
the size
r
s
. Let
x
be the horizontal coordinate of the pixel and
y
be the vertical
coordinate (
x
=1,
,
s
). For each value of
x
and
y
are introduced the
corresponding masks
M
x
and
M
y
, which are the “neural codes” of the corresponding
coordinate. Then the code of the feature
i
, which has on the image the coordinates
x
i
and
y
i
, is equal to
...
,
r
;
y
=1,
...
Z
X
i
;
y
i
¼
M
i
&
M
x
i
&
M
y
i
;
(6.12)
where & is the bitwise logical “AND.”
The code of the handwritten symbol will be determined by the expression:
Z
c
¼
U
i
Z
x
i
;
y
i
;
(6.13)
where U is step-by-step “OR” and is carried out for all features extracted on the
image of the object.
To form the codes for
x
and
y
coordinates, a procedure is used that makes it
possible to obtain the correlated masks. This means that the masks for coordinates
differing little from each other have a large quantity of common unit elements, but
the masks of the coordinates with more differences have few common unit
